Two theorems give sufficient shallow-network width to reach a prescribed error in a Fréchet metric of semi-norms, applied to exponential spectral Barron, Gelfand-Shilov, and bandlimited (Paley-Wiener type) symbol classes.
Liftings for ultra-modulation spaces, and one-parameter groups of gevrey-type pseudo-differential operators,
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Approximation Rates in Fr\'echet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers
Two theorems give sufficient shallow-network width to reach a prescribed error in a Fréchet metric of semi-norms, applied to exponential spectral Barron, Gelfand-Shilov, and bandlimited (Paley-Wiener type) symbol classes.